How to deform armature and keep its volume?
If I understand correctly, you try to move your arm with an armature but the bone deforms the arm too much and you want to correct the proportions.
To do so I think you need to use Shapekeys and Drivers, Shapekeys will allow you to correct the shape and Drivers will allow your bone to control the shapekey value:

Create your mesh and armature, parent the mesh to the armature With Automatic Weight, in the Armature modifier enable the Display Edit Mode and the On Cage options, bend the arm the way you want, in Object mode create 2 shapekeys for your mesh, select the second shapekey, go in Edit mode and modify the mesh so that it gets the shape you want:



Back to Object mode, right click on the Shapekey Value and click on Add Driver, it opens a panel, in this panel &gt; Object &gt; choose the armature and the arm bone, Type &gt;  choose the type of transformation the bone will affect (here Z Rotation), and Space &gt; Local Space:




Click on the Shapekey Value again and this time choose Open Drivers Editor, you should see the driver curve, select all and type V to make the curve straight, rotate the curve until you're satisfied of its effect on the mesh. Now when you'll rotate the arm the mesh will bend and also apply the shapekey you've created.